Orla McGrath (University of Leeds) – TBA
TBA
Algebra
During term-time, we hold an Algebra Seminar at 3pm on Tuesdays.
In this page, you can find all the information on the seminar (currently organised by Francesca Fedele, Ilaria Colazzo and Peter Huston) since September 2025.
Unless otherwise specified, Algebra seminars take place during term time on Tuesdays at 3.00pm in the MALL, School of Mathematics, University of Leeds.
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Peter Huston (University of Leeds) – TBA
TBA
Andrei Marshakov (HSE University) – Decorated Newton polygons and reductions of cluster integrable systems
I start with the definition of cluster integrable systems a la Goncharov and Kenyon, defined by convex Newton polygons, up to the action of $SA(2,\mathbb{Z})$. There are several arguments requiring that to complete the picture, this class should be extended by their Hamiltonian reductions, which can be performed preserving the structure of cluster variety.
Duncan Laurie (University of Edinburgh) – TBA
TBA
Florian Eisele (University of Manchester) – Block theory of profinite groups
Profinite groups are a class of topological groups with close ties to finite groups. Many of the questions around group rings of finite groups and their representation theory have profinite analogues. I will report on results that generalise block fusion systems and Puig's theory of nilpotent blocks to the profinite setting, and a resulting description of blocks with infinite dihedral defect groups. This is joint work with MacQuarrie and Franquiz Flores.
Michael Wibmer (University of Leeds) – Trivializing torsors for difference algebraic groups
A torsor, also known as a principal homogeneous space, is an algebraic variety with a simply transitive action of an algebraic group. These play a main role in the arithmetic theory of algebraic groups and an important question is to find conditions that guarantee that the torsor is trivial, i.e., isomorphic to the algebraic group itself with action given by left multiplication. In this talk we will discuss analogous questions in the realm of difference algebraic geometry, i.e., instead of just algebraic equations, we allow difference algebraic equations in the definition of our groups and varieties.
This is joint work with Annette Bachmayr.
Marco Bertola (Concordia University) – The r-matrix structure in higher genus
On the space of matrices with rational (trigonometric/elliptic) entries there is a well-known Lie-Poisson structure, the ``r-matrix structure’’. It is an essential structure underlying the Hamiltonian dynamics of the vast majority of integrable systems, isospectral and isomonodromic evolution equations. The known r-matrices depend on parameter in rational way (trig/elliptic, respectively) and hence we think of them on the Riemann sphere (cylinder/torus).
In a relatively abstract Hamiltonian framework the isospectral evolution equations are generalized to higher genus Riemann surfaces as the “Hitchin systems”, an evolutionary integrable system on the moduli space of vector bundles. On the isomonodromic side main progress is attributable to Krichever who used a quite explicit coordinatization of vector bundles on Riemann surfaces that we can call “Tyurin parametrization”.
In this talk I report on the fully explicit generalization of the r-matrix structure to an arbitrary genus Riemann surface merging the Tyurin-Krichever approach with the general framework of Hitchin’s. The key tool is a (fully explicit) matrix-valued kernel that plays crucial role also in setting up integral equations in related area of the "non-abelian steepest descent” method.
Baoyu Zhang (University of Birmingham) – Fusion systems and essential subgroups
Local finite group theory has been an important topic, particularly via the Classification of Finite Simple Groups. Fusion systems are categories defined on p-groups, which have helped simplify and extend much of the theory in the last 20 years and are starting to link group theory, representation theory, and algebraic topology. By Alperin-Goldschmidt's fusion theorem, a saturated fusion system can be completely determined by its essential subgroups. In this talk, I will discuss fusion systems with two-generator essential subgroups and present some other results on fusion systems.
Silvia Properzi (Vrije Universiteit Brussel) – Skew Braces, the YBE, and some results in the classification of solutions
This talk explores the interplay between algebraic structures known as skew braces and set-theoretic solutions to the Yang–Baxter equation (YBE), a central object in mathematical physics and quantum group theory. Skew braces provide a powerful framework for constructing and analysing solutions.
We focus on involutive solutions, in particular on their permutation skew braces that allow for explicit computations and structural analysis.
We introduce the necessary background on skew braces and the YBE, we study the role of the permutation skew brace, which captures essential symmetries of solutions and serves as an effective invariant. As a concrete application, we present a full classification, up to isomorphism, of all involutive solutions of size $p^2$, where $p$ is a prime.
Anja Sneperger (University of Leeds) – Some determinants and relations in Heronian friezes
Motivated by computational geometry of point configurations on the Euclidean plane, and by the theory of cluster algebras of type A, Sergey Fomin and Linus Setiabrata have recently introduced Heronian friezes - the Euclidean analogues of Coxeter’s frieze patterns. I will explain the way these friezes arise from a polygon in the complex plane, and that a sufficiently generic Heronian frieze is uniquely determined by a small proportion of its entries. Then, I shall proceed to some of my results, that hold in the cyclic case, i.e. when the vertices of the polygon are placed on the circle. Namely, I will speak about vanishing of certain determinants in the cyclic case, as well as explain some interesting algebraic relations that hold between the entries of the cyclic Heronian frieze.